Mathematical economics and finance

Additional Info

  • ECTS credits: 6
  • Semester: 1
  • University: University of L'Aquila
  • Prerequisites:

    I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.

  • Objectives:

    On successful completion of this course, the student should:

    - Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.

    - Explain some interconnections among these various results.

    - Apply this analysis to game and economic theory

  • Topics:

    Sperner’s lemma

    The Knaster-Kuratowski-Mazurkiewicz lemma

    Brouwer's fixed point theorem

    Variational inequalities and equilibrium problems

    Generalized monotonicity and convexity

    Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle

    Continuity of correspondences

    Browder, Kakutani and Fan-Glicksberg fixed point theorems

    Gale-Nikaido-Debreu theorem

    Nash equilibrium of games and abstract economies

    Walrasian equilibrium of an economy

    An application to traffic network

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